As per the title, can airlines recover costs if they dump fuel due to a medical emergency on board shortly after takeoff?
You are overestimating (by asking) the cost of fuel in such a worst-case scenario diversion that requires fuel dumping.
With this week's jet fuel price, 50 tonnes (approx. half of what is loaded on a 787 bound for a long-haul) would set you back \$31,000.[a] But,
A single flight diversion can cost Emirates anything from US\$50,000 to over US\$600,000, depending on the nature of the diversion which includes fuel, flight catering, landing and ground handling fees, air navigation cost, passenger rebooking costs and onward connection, as well as other associated costs to care for crew and passengers.
Since 50 tonnes can be considered an upper limit, and Emirates' upper limit is \$600,000, fuel is just 5% of the cost. Further,
Adel Al Redha, Emirates' Executive Vice President and Chief Operating Officer, said: "We can never hope to recover the costs of a flight diversion, but the wellbeing of our customers is always our number one priority (...) [emphasis added]
Source: Emirates reveals the real cost of medical diversions for an airline, www.airlineratings.com, 2017
[a]: Also, for reference: An A380 returned to SFO not long into a flight due to a medical emergency, and dumped "40 tons" on the way back (avherald.com).